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L\"uscher established a non-perturbative formula to extract the elasticscattering phases from two-particle energy spectrum in a torus using latticesimulations. Rummukainen and Gottlieb further extend it to the moving frame,which is devoted to the system of two identical particles. In this work, wegeneralize Rummukainen-Gottlieb's formula to the generic two-particle systemwhere two particles are explicitly distinguishable, namely, the masses of thetwo particles are different. The finite size formula are achieved for both$C_{4v}$ and $C_{2v}$ symmetries. Our analytical results will be very helpfulfor the study of some resonances, such as kappa, vector kaon, and so on.

Rummukainen-Gottlieb's formula on two-particle system with different mass